The lliquid films are applied in the various equipments intended for an intensification of heat and mass transfer processes. Heat transfer can also be intensifying by the gas flow above the liquid surface; these processes take a place at two-phase flows in mini- and microchannels. This study deals with the heat transfer in a locally heated liquid film of constant thickness h. The film is supposed to flow along the heated plate having constant temperature TW under the action of gravity and a gas flow. Influence of a gas flow on a velocity profile in the liquid is considered through shear stress on an interface. Coefficient of heat exchange and shear stress on a film surface suppose be set. Equation of the energy for a liquid film is solved by Galerkin technique which is special case of the weighed residuals method (WRM). Applying of Galerkin technique to this problem allows calculating the temperature in a liquid analytically for arbitrary a temperature profile in initial cross-section of a film. For initial temperature profile, gained from the analytical solution the temperature field is calculated. Results of these calculations are compared to results of numerical solution of the energy equation by finite-difference method. This comparison has shown the good agreement both for a falling film, and for cocurrent or countercurrent gas flow.
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